Machine Design

Nonlinear FEA 101

Fast computers, refined nonlinear solvers, and intuitive interfaces are making nonlinear FEA easier to use.

This Algor MES of a conveyor-belt assembly uses a nonlinear hyperelastic material model for the belt. This simulation lets engineers study the belt's response during tensioning. Linear-static stress analysis could not have accurately represented the hyperelastic material.
The stress-strain plot for curve A is typical for most metals. The term linear in linear-static analysis refers to the early or straight-line portion of the curve. Material behavior is predictable here. Curve B represents some alloys, elastomers, and plastics. This type of curve is inherently nonlinear. Curve C shows how human soft tissue behaves. Applying linear analysis to materials represented by curves B and C would call for skilled interpretations.
Engineers at SiWave Inc. examined the dynamic response of this MEMS optical switch using Algor MES. The simulation was to assure the device would comply with Telcordia shock-loading standards. The analysis calculated motion, stresses, and displacements throughout the event. A linear-static-stress analysis could only have calculated results for one moment in time.
Engineers at West Coast Engineering Group Ltd. used Algor MES to simulate a car hitting a utility pole. MES calculated the motion of the car, buckling in the pole that resulted from the crash, and stresses at each time step of the event. Results aided engineers in determining how impact stresses were distributed in the pole's base plate.

Michael L. Bussler
President and CEO
Algor Inc.
Pittsburgh, Pa.

When it comes to analyses, engineers use linear-static finite element analysis more often than any other. That's partly because they believe nonlinear and dynamic analyses take too much time and require greater expertise. True, they may require a little more study than linear-static-stress analysis. But most engineering problems contain some type of nonlinear effect. Handling these effects with simplified linear approximations may take less processing time, but provides results that are not always valid.

The good news is that barriers to nonlinear analysis are coming down thanks to faster computers, refined nonlinear solvers, and intuitive user interfaces. To find out if it's time to go nonlinear, answer the following questions.

- Does the problem involve only linear characteristics? That is, does it have no nonlinear material properties, large deformations, or motion?
- Are loads static and accurately quantified?
- Do you thoroughly understand how the simplifications of static-stress analyses affect results?

Answering "no" to any one means you are a candidate for nonlinear analysis.

The most obvious time to step beyond linear-static-stress analysis is when working with materials that have nonlinear material properties, such as plastics and rubber. Their stress-strain curves are inherently nonlinear. In such cases, it only makes sense to use a nonlinear material model. Once selected, software is often smart enough to prompt users for additional data through Windows-native dialog boxes.

For example, when considering parts made of a material that might yield under load, use a model capable of simulating plasticity, such as von Mises with isotropic or kinematic hardening. To complement the model, well-designed software will ask for specific material properties for linear portions of the stress-strain curve and other properties farther out on the curve, where part strength is lower.

Large or permanent deformations are another reason to consider nonlinear analysis. Large deformations include local and snap-through buckling. These events are called geometric nonlinearities. Nonlinear analyses produce more accurate results than linear analyses when loading produces concentrated stress values. Stress concentrations are usually near constraints or around small geometric features, such as fillets and holes. A loss of accuracy in linear-static-stress analyses comes from stresses based on an object's initial shape, whereas nonlinear analysis determines stresses based on an object's deformed shape.

Adding motion to the mix is another reason to step beyond linear-static-stress analyses. Most designs do move. FEA-based simulation methods that combine large-scale motion and stress analysis, such as Algor's Mechanical Event Simulation (MES) software, incorporate both material and geometric nonlinearities. This type of simulation accounts for bending, twisting, stretching, squashing, and inertial effects of FEA models, and shows motion and its results, such as impact, buckling, and permanent deformation.

Even when designs won't undergo significant motion, consider nonlinear analysis to properly account for how "static" loads are applied. This action can greatly exaggerate the stresses that designs must withstand. For example, linear analysis of a table may confirm it can withstand the pressure of a 50-lb weight. Indeed, gently placing 50 lb on the table would probably cause no significant deformation. But dropping the weight onto the table could produce a large deformation.

Engineers are sometimes able to draw from their experience and expertise to build products that withstand estimated and calculated forces. However, approximate forces and safety factors often require more expertise than using software tools to simulate real-world events.

MES results are based on physical data, as well as dynamic and contact forces, instead of calculated and assumed loads and constraints. Linear analyses, on the other hand, are only as accurate as the applied loads and constraints. It's time consuming and error prone to find loads from hand calculations, physical tests, and overestimating or guessing based on experience.

Fortunately, advances in user interfaces have made nonlinear and motion simulations easier to set up and more accessible to engineers and designers. Some FEA vendors provide nonlinear and motion capabilities within the same interface as linear-static-stress analysis and include full associativity with leading CAD solid modelers and wizards that help users perform common tasks. Such interfaces often use standard engineering terminology and visual guidance through the process, so users can focus on the physics of a part or assembly, rather than trying to master the terminology of a particular motion-analysis software. Distance-learning Web courses provide more direction on using these types of analyses. Traditional classroom seminars are another way to learn analysis techniques and have the benefit of letting students bring real-world experiences to the class. (See "Planning for FEA training" Machine Design, May 8, 2003, p. 48-50.)

Regardless of how you approach learning nonlinear and motion simulation, remember the three indicators of nonlinear conditions: material nonlinearity, potential for geometric nonlinearity, and motion. Simulating real-world nonlinear effects means more accurate results, fewer physical prototypes, shorter time to market, and better, safer products at a lower cost.

Make contact:

Algor Inc., (412) 967-2700,

SiWave, (888) 868-8902,

West Coast Engineering Group Ltd., (604) 946-1256,
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